Question 1 (essay worth 10 points) (08.01 mc) the graph shows two lines, a and b. a graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. a straight line labeled a joins the ordered pair 2, 6 with the ordered pair 5, 0. another straight line labeled b joins the ordered pair 0, 2 with the ordered pair 6, 6. part a: how many solutions does the pair of equations for lines a and b have? explain your answer. (5 points) part b: what is the solution to the equations of lines a and b? explain your answer. (5 points)

Part A) The system has one solution

Part B) The solution is the point (2.54,3.69)

Step-by-step explanation:

step 1

Find the equation of line A

Find the slope

we have

(2,6) and (5,0)

m=(0-6)/(5-2)=-6/4=-1.5

Find the equation of the line

with the slope m and point (5,0)

y-0=-1.5(x-5)

y=-1.5x+7.5 -----> equation A

step 2

Find the equation of line B

Find the slope

we have

(0,2) and (6,6)

m=(6-2)/(6-0)=4/6=2/3

Find the equation of the line

with the slope m and point (0,2)

y-2=(2/3)(x-0)

y=(2/3)x+2 -----> equation B

step 3

Solve the system of equations

y=-1.5x+7.5 -----> equation A

y=(2/3)x+2 -----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

The system has one point of intersection

therefore

The system has only one solution

The solution is the point (2.54,3.69)

see the attached figure